ODE
\[ x^7 y(x)^2 y'(x)^3+\left (1-3 x^6 y(x)^3\right ) y'(x)^2+3 x^5 y(x)^4 y'(x)-x^4 y(x)^5=0 \] ODE Classification
[[_homogeneous, `class G`]]
Book solution method
Change of variable
Mathematica ✗
cpu = 599.999 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 1.051 (sec), leaf count = 4164 \[ \text {Too large to display} \] Mathematica raw input
DSolve[-(x^4*y[x]^5) + 3*x^5*y[x]^4*y'[x] + (1 - 3*x^6*y[x]^3)*y'[x]^2 + x^7*y[x]^2*y'[x]^3 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(x^7*y(x)^2*diff(y(x),x)^3+(1-3*x^6*y(x)^3)*diff(y(x),x)^2+3*x^5*y(x)^4*diff(y(x),x)-x^4*y(x)^5 = 0, y(x),'implicit')
Maple raw output
y(x)^3-4/27/x^6 = 0, Int((-6*(-108*y(x)^6*_a^12+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(1/3)*_a^6*y(x)^3+24*_a^6*y(x)^3+2*(-108*y(x)^6*_a^12+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(1/3)-(-108*y(x)^6*_a^12+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(2/3)-4)/_a/(18*(-108*y(x)^6*_a^12+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(1/3)*_a^6*y(x)^3-24*_a^6*y(x)^3+(-108*y(x)^6*_a^12+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(2/3)-2*(-108*y(x)^6*_a^12+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(1/3)+4),_a = _b .. x)+Intat(6*(-108*_f^6*x^12+12*3^(1/2)*(1/_f*(27*_f^3*x^6-4))^(1/2)*_f^5*x^9+72*x^6*_f^3-8)^(1/3)*x^6*_f^2/(18*(-108*_f^6*x^12+12*3^(1/2)*(1/_f*(27*_f^3*x^6-4))^(1/2)*_f^5*x^9+72*x^6*_f^3-8)^(1/3)*x^6*_f^3-24*x^6*_f^3+(-108*_f^6*x^12+12*3^(1/2)*(1/_f*(27*_f^3*x^6-4))^(1/2)*_f^5*x^9+72*x^6*_f^3-8)^(2/3)-2*(-108*_f^6*x^12+12*3^(1/2)*(1/_f*(27*_f^3*x^6-4))^(1/2)*_f^5*x^9+72*x^6*_f^3-8)^(1/3)+4)-Int(-31104*_a^5*((_a^6*_f^3-1/24*(-108*_f^6*_a^12+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)-1/6)*_a^6*_f^3*(3^(1/2)*_f*_a^3*(_a^6*_f^3+2/27)/(1/_f*(27*_a^6*_f^3-4))^(1/2)-2*_a^6*_f^3+5/27*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^2*_a^3+2/3)/(-108*_f^6*_a^12+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)+1/12*(-108*_f^6*_a^12+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)*(-1/72*(-108*_f^6*_a^12+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)+_a^6*_f^3*(3^(1/2)*_f*_a^3*(_a^6*_f^3+2/27)/(1/_f*(27*_a^6*_f^3-4))^(1/2)-2*_a^6*_f^3+5/27*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^2*_a^3+2/3)/(-108*_f^6*_a^12+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)+1/36*(-108*_f^6*_a^12+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)-1/18))*_f^2/(18*(-108*_f^6*_a^12+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)*_a^6*_f^3-24*_a^6*_f^3+(-108*_f^6*_a^12+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)-2*(-108*_f^6*_a^12+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)+4)^2,_a = _b .. x),_f = y(x))+_C1 = 0, Int(((-I*3^(1/2)-1)*(-108*y(x)^6*_a^12+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(2/3)+(12*_a^6*y(x)^3-4)*(-108*y(x)^6*_a^12+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(1/3)-24*(_a^6*y(x)^3-1/6)*(I*3^(1/2)-1))/_a/(24*I*3^(1/2)*_a^6*y(x)^3-36*(-108*y(x)^6*_a^12+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(1/3)*_a^6*y(x)^3-24*_a^6*y(x)^3+I*(-108*y(x)^6*_a^12+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(2/3)*3^(1/2)+(-108*y(x)^6*_a^12+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(2/3)-4*I*3^(1/2)+4*(-108*y(x)^6*_a^12+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(1/3)+4),_a = _b .. x)+Intat(-12*(-108*_f^6*x^12+12*3^(1/2)*(1/_f*(27*_f^3*x^6-4))^(1/2)*_f^5*x^9+72*x^6*_f^3-8)^(1/3)*x^6*_f^2/(24*I*3^(1/2)*x^6*_f^3-36*(-108*_f^6*x^12+12*3^(1/2)*(1/_f*(27*_f^3*x^6-4))^(1/2)*_f^5*x^9+72*x^6*_f^3-8)^(1/3)*x^6*_f^3-24*x^6*_f^3+I*(-108*_f^6*x^12+12*3^(1/2)*(1/_f*(27*_f^3*x^6-4))^(1/2)*_f^5*x^9+72*x^6*_f^3-8)^(2/3)*3^(1/2)+(-108*_f^6*x^12+12*3^(1/2)*(1/_f*(27*_f^3*x^6-4))^(1/2)*_f^5*x^9+72*x^6*_f^3-8)^(2/3)-4*I*3^(1/2)+4*(-108*_f^6*x^12+12*3^(1/2)*(1/_f*(27*_f^3*x^6-4))^(1/2)*_f^5*x^9+72*x^6*_f^3-8)^(1/3)+4)-Int(-62208*_a^5*(_a^6*((1/24*I*3^(1/2)+1/24)*(-108*_f^6*_a^12+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)+(I*3^(1/2)-1)*(_a^6*_f^3-1/6))*_f^3*(3^(1/2)*_f*_a^3*(_a^6*_f^3+2/27)/(1/_f*(27*_a^6*_f^3-4))^(1/2)-2*_a^6*_f^3+5/27*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^2*_a^3+2/3)/(-108*_f^6*_a^12+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)-1/12*(-108*_f^6*_a^12+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)*((-1/72*I*3^(1/2)-1/72)*(-108*_f^6*_a^12+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)+(I*3^(1/2)+1)*_a^6*_f^3*(3^(1/2)*_f*_a^3*(_a^6*_f^3+2/27)/(1/_f*(27*_a^6*_f^3-4))^(1/2)-2*_a^6*_f^3+5/27*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^2*_a^3+2/3)/(-108*_f^6*_a^12+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)+1/18*I*3^(1/2)-1/18*(-108*_f^6*_a^12+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)-1/18))*_f^2/(24*I*3^(1/2)*_a^6*_f^3-36*(-108*_f^6*_a^12+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)*_a^6*_f^3-24*_a^6*_f^3+I*(-108*_f^6*_a^12+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)*3^(1/2)+(-108*_f^6*_a^12+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)-4*I*3^(1/2)+4*(-108*_f^6*_a^12+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)+4)^2,_a = _b .. x),_f = y(x))+_C1 = 0, Int(((-I*3^(1/2)+1)*(-108*y(x)^6*_a^12+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(2/3)+(-12*_a^6*y(x)^3+4)*(-108*y(x)^6*_a^12+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(1/3)-24*(_a^6*y(x)^3-1/6)*(I*3^(1/2)+1))/_a/(24*I*3^(1/2)*_a^6*y(x)^3+36*(-108*y(x)^6*_a^12+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(1/3)*_a^6*y(x)^3+24*_a^6*y(x)^3+I*(-108*y(x)^6*_a^12+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(2/3)*3^(1/2)-(-108*y(x)^6*_a^12+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(2/3)-4*I*3^(1/2)-4*(-108*y(x)^6*_a^12+12*3^(1/2)*(1/y(x)*(27*_a^6*y(x)^3-4))^(1/2)*y(x)^5*_a^9+72*_a^6*y(x)^3-8)^(1/3)-4),_a = _b .. x)+Intat(12*(-108*_f^6*x^12+12*3^(1/2)*(1/_f*(27*_f^3*x^6-4))^(1/2)*_f^5*x^9+72*x^6*_f^3-8)^(1/3)*x^6*_f^2/(24*I*3^(1/2)*x^6*_f^3+36*(-108*_f^6*x^12+12*3^(1/2)*(1/_f*(27*_f^3*x^6-4))^(1/2)*_f^5*x^9+72*x^6*_f^3-8)^(1/3)*x^6*_f^3+24*x^6*_f^3+I*(-108*_f^6*x^12+12*3^(1/2)*(1/_f*(27*_f^3*x^6-4))^(1/2)*_f^5*x^9+72*x^6*_f^3-8)^(2/3)*3^(1/2)-(-108*_f^6*x^12+12*3^(1/2)*(1/_f*(27*_f^3*x^6-4))^(1/2)*_f^5*x^9+72*x^6*_f^3-8)^(2/3)-4*I*3^(1/2)-4*(-108*_f^6*x^12+12*3^(1/2)*(1/_f*(27*_f^3*x^6-4))^(1/2)*_f^5*x^9+72*x^6*_f^3-8)^(1/3)-4)-Int(62208*_a^5*_f^2*(_a^6*((1/24*I*3^(1/2)-1/24)*(-108*_f^6*_a^12+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)+(I*3^(1/2)+1)*(_a^6*_f^3-1/6))*_f^3*(3^(1/2)*_f*_a^3*(_a^6*_f^3+2/27)/(1/_f*(27*_a^6*_f^3-4))^(1/2)-2*_a^6*_f^3+5/27*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^2*_a^3+2/3)/(-108*_f^6*_a^12+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)-1/12*((-1/72*I*3^(1/2)+1/72)*(-108*_f^6*_a^12+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)+_a^6*(I*3^(1/2)-1)*_f^3*(3^(1/2)*_f*_a^3*(_a^6*_f^3+2/27)/(1/_f*(27*_a^6*_f^3-4))^(1/2)-2*_a^6*_f^3+5/27*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^2*_a^3+2/3)/(-108*_f^6*_a^12+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)+1/18*I*3^(1/2)+1/18*(-108*_f^6*_a^12+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)+1/18)*(-108*_f^6*_a^12+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3))/(24*I*3^(1/2)*_a^6*_f^3+36*(-108*_f^6*_a^12+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)*_a^6*_f^3+24*_a^6*_f^3+I*(-108*_f^6*_a^12+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)*3^(1/2)-(-108*_f^6*_a^12+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(2/3)-4*I*3^(1/2)-4*(-108*_f^6*_a^12+12*3^(1/2)*(1/_f*(27*_a^6*_f^3-4))^(1/2)*_f^5*_a^9+72*_a^6*_f^3-8)^(1/3)-4)^2,_a = _b .. x),_f = y(x))+_C1 = 0